The only situation in which a hospital is required to treat you - public hospitals included - is if you go to ER and are not in a stable condition. They will not provide e.g. medicine for lifelong chronic conditions, or the tests required to make sure that medicine isn't killing you until you're practically already dead. They won't provide necessary surgery unless you're literally about to die from not having it. They won't provide psychiatric help. It is not a treatment option for anything except a car crash or severe acute illness.
